Generally, it is old to provide a subsurface safety valve system having a plurality of valves, one of which opens on high tubing pressure and the other which closes on low tubing pressure. For example, see U.S. Pat. Nos. 3,749,119 and 3,672,397.The present invention is directed to an improved safety valve having a single valve closure member which is actuated by a tubular member for providing straight through flow. The tubular member is acted upon by an abnormal or predetermined high tubing pressure or an abnormal or predetermined low tubing pressure to actuate the valve closure member to a closed position.